Reference documentation for deal.II version 9.3.0

#include <deal.II/lac/solver_fire.h>
Classes  
struct  AdditionalData 
Public Types  
using  vector_type = VectorType 
Public Member Functions  
SolverFIRE (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory, const AdditionalData &data=AdditionalData())  
SolverFIRE (SolverControl &solver_control, const AdditionalData &data=AdditionalData())  
template<typename PreconditionerType = DiagonalMatrix<VectorType>>  
void  solve (const std::function< double(VectorType &, const VectorType &)> &compute, VectorType &x, const PreconditionerType &inverse_mass_matrix) 
template<typename MatrixType , typename PreconditionerType >  
void  solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner) 
boost::signals2::connection  connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate)> &slot) 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Subscriptor functionality  
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.  
void  subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
void  unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
unsigned int  n_subscriptions () const 
template<typename StreamType >  
void  list_subscribers (StreamType &stream) const 
void  list_subscribers () const 
Static Public Member Functions  
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Protected Member Functions  
virtual void  print_vectors (const unsigned int, const VectorType &x, const VectorType &v, const VectorType &g) const 
Protected Attributes  
const AdditionalData  additional_data 
GrowingVectorMemory< VectorType >  static_vector_memory 
VectorMemory< VectorType > &  memory 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate), StateCombiner >  iteration_status 
FIRE (Fast Inertial Relaxation Engine) for minimization of (potentially nonlinear) objective function \(E(\mathbf x)\), \(\mathbf x\) is a vector of \(n\) variables ( \(n\) is the number of variables of the objective function). Like all other solver classes, it can work on any kind of vector and matrix as long as they satisfy certain requirements (for the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class). The type of the solution vector must be passed as template argument, and defaults to Vector<double>.
FIRE is a damped dynamics method described in Structural Relaxation Made Simple by Bitzek et al. 2006, typically used to find stable equilibrium configurations of atomistic systems in computational material science. Starting from a given initial configuration of the atomistic system, the algorithm relies on inertia to obtain (nearest) configuration with least potential energy.
Notation:
Given initial values for \(\Delta t\), \(\alpha = \alpha_0\), \(\epsilon\), \(\mathbf x = \mathbf x_0\) and \(\mathbf v= \mathbf 0\) along with a given mass matrix \(\mathbf M\), FIRE algorithm is as follows,
Also see EnergyMinimization in AtomictoContinuum ScaleBridging Methods by Eidel et al. 2011.
Definition at line 89 of file solver_fire.h.

inherited 
SolverFIRE< VectorType >::SolverFIRE  (  SolverControl &  solver_control, 
VectorMemory< VectorType > &  vector_memory,  
const AdditionalData &  data = AdditionalData() 

) 
Constructor.
SolverFIRE< VectorType >::SolverFIRE  (  SolverControl &  solver_control, 
const AdditionalData &  data = AdditionalData() 

) 
Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.
void SolverFIRE< VectorType >::solve  (  const std::function< double(VectorType &, const VectorType &)> &  compute, 
VectorType &  x,  
const PreconditionerType &  inverse_mass_matrix  
) 
Obtain a set of variables x
that minimize an objective function described by the polymorphic function wrapper compute
, with a given preconditioner inverse_mass_matrix
and initial x
values. The function compute
returns the objective function's value and updates the objective function's gradient (with respect to the variables) when passed in as first argument based on the second argument– the state of variables.
void SolverFIRE< VectorType >::solve  (  const MatrixType &  A, 
VectorType &  x,  
const VectorType &  b,  
const PreconditionerType &  preconditioner  
) 
Solve for x that minimizes \(E(\mathbf x)\) for the special case when \(E(\mathbf x) = \frac{1}{2} \mathbf x^{T} \mathbf A \mathbf x  \mathbf x^{T} \mathbf b\).

protectedvirtual 
Interface for derived class. This function gets the current iteration x
(variables), v
(x's time derivative) and g
(the gradient) in each step. It can be used for graphical output of the convergence history.

inlineinherited 
Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.
slot  A function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration. 

inherited 
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 136 of file subscriptor.cc.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 156 of file subscriptor.cc.

inlineinherited 
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 301 of file subscriptor.h.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 318 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 204 of file subscriptor.cc.

inlineinherited 
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 310 of file subscriptor.h.

protected 
Additional data to the solver.
Definition at line 179 of file solver_fire.h.

mutableprotectedinherited 

protectedinherited 

protectedinherited 
A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.
The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.